Tara bicycles 15 mph with no wind. Against the wind, she bikes 10 miles in the same time that it takes to bike 16 miles with the wind. What is the speed of the wind?

3.46 mph

Step-by-step explanation:

Speed of Tara bicycling without wind effect = 15mph

let the speed of wind be x mph

If she cycles against the wind then her speed will be decrease by the amount as the speed of wind

Then,

Speed of Tara bicycling against wind effect = (15-x)mph

distance traveled by Tara against wind = 10 miles

we know that

time = distance by speed

time taken by Tara while traveling against wind = 10/(15-x)

If she cycles with the wind then her speed will be increase by the amount as the speed of wind

Then,

Speed of Tara bicycling with wind effect = (15+x)mph

distance traveled by Tara w wit wind = 16 miles

time taken by Tara while traveling with wind = 16/(15+x)

it is given that both the time are same

time taken by Tara while traveling with wind  = time taken by Tara while traveling against wind

16/(15+x) = 10/(15-x)

=> 16(15-x)=10(15+x)

=> 240 - 16x = 150 +10x

=>240 - 150 = 10x+16x

=> 90 = 26x

=> x = 90/26 = 3.46

Thus, speed of wind is 3.46 mph.

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